Local gate control of Mott metal-insulator transition in a 2D metal-organic framework

Electron-electron interactions in materials lead to exotic many-body quantum phenomena, including Mott metal-insulator transitions (MITs), magnetism, quantum spin liquids, and superconductivity. These phases depend on electronic band occupation and can be controlled via the chemical potential. Flat bands in two-dimensional (2D) and layered materials with a kagome lattice enhance electronic correlations. Although theoretically predicted, correlated-electron Mott insulating phases in monolayer 2D metal-organic frameworks (MOFs) with a kagome structure have not yet been realised experimentally. Here, we synthesise a 2D kagome MOF on a 2D insulator. Scanning tunnelling microscopy (STM) and spectroscopy reveal a MOF electronic energy gap of ∼200 meV, consistent with dynamical mean-field theory predictions of a Mott insulator. Combining template-induced (via work function variations of the substrate) and STM probe-induced gating, we locally tune the electron population of the MOF kagome bands and induce Mott MITs. These findings enable technologies based on electrostatic control of many-body quantum phases in 2D MOFs.

iii) The synthesis of a 2D-MOF on h-BN via supramolecular coordination chemistry is not new (see ref. 30).In addition, the gate control of the DCA3Cu2 2D-MOF electronic structures and charging was also already performed on graphene (ref. 31).iv) page 3 (lines 84-85) "a crystalline MOF domain" growth is claimed.However, compared to ref. 31, this is far from crystalline.As shown in Fig. 1(a) of the manuscript, the MOF domain is surrounded by excess DCA molecules, therefore the 3:2 stoichiometry was only successfully achieved on rather small regions of the sample (50 × 50 nm2).In addition, white islands embedded into the 2D-MOF domains may point out to excess Cu islands.Can the authors identify such islands?There are also many additional defects in the MOF domain which are not discussed (black or dark blue points, wires or regions inside the domain).It is therefore almost impossible to find more than two h-BN pore regions together, covered by defect free DCA3Cu2 2D-MOF.The authors should provide experimental evidence of a long-range ordered growth of the 2D MOF.Otherwise, the authors should discuss the defects appearing in the 2D-MOF domains, as well as their limitations to achieve a highly crystalline 2D-MOF growth.This is an important point since such small domain sizes and high defect density will preclude the use of such 2D-MOFs in electronic devices.v) page 4 (line 87).Here the growth of the 2D-MOF on top of the h-BN/Cu(111) electronic moiré is presented.However, it is known that the moiré periodicity can change approximately from 3 nm to 14 nm on the h-BN/Cu(111) samples grown with borazine in UHV (ref. 30).Is there any moiré periodicity preference for the successful growth of 2D-MOF islands on top?The authors should provide a discussion in this regard.vi) page 4 (lines 102-105): The authors should be transparent and mention that DCA3Cu2 2D-MOF (the very same systems as the one shown here) has already been grown (as a full monolayer) on top of a rather good decoupling layer of graphene on Ir(111) (ref. 31).
vii) With respect to Figure 1.The authors only focus on the kagome band structure close to the Fermi level.However, it is known that more kagome bands should appear above and below the energy range considered here (ref.19).Can the authors comment on this point?Do the authors have DFT calculations for a wider energy range?How does the band structure of the Mott insulating phase look like?
viii) The authors should provide STS performed on a larger voltage range (for instance from -2V to +2V) to see what happens to the additional kagome bands away from the Fermi level.Is there any strong molecular HOMO/LUMO or 2D-MOF valence/conduction band feature at lower/higher voltages, as already observed in ref. 33 and in A. Kumar et al. Nano Letters 18, 5596 (2018).The latter reference should be added since DCA3Co2 2D-MOF was grown on the rather good decoupling graphene layer on Ir(111), whereby a 2D-MOF band structure signature was already observed.ix) page 6 (line 149) "the high crystalline growth makes a large disorder-related gap unlikely".If this is the case, how does the STS look at different points of the 2D-MOF island?Are the features identical if one performs STS on the dark pore regions?How do the electronic properties look like at the edge of the 2D-MOF domain?At which position does the domain edge already play a role in disturbing the reported electronic properties?
x) With respect to Figure 2. Why are the spectra asymmetric?Why not show dI/dV maps at particular energies instead of STM images?xi) page 6 (lines 157-162): Figure 3 should be explained in more detail in the manuscript, specially panels 3e and 3f.The order of the figure description should be changed in the text (a, b, c….).Regarding panel 3b, apart from the theoretically predicted peak at the Fermi level, which can not be captured experimentally, there are many additional peaks in the unoccupied region (>0.2V).These peaks or modulations are not present in the theoretical simulations.What are they?They have a similar amplitude to the relevant peaks close to the Fermi level, therefore, most probably are not artefacts.The authors should describe them.
xii) Figure 3a,b.The authors perform STS at Cu adatom positions.For completeness, the authors should also perform the same STS sequence at the DCA anthracene lobe positions.Does the same Mott metal-insulator transition appear or evolve in the same fashion as on the Cu adatoms?xiii) Figure 3. Since the Mott metal-insulator transition is highly dependent on the work function variation of the h-BN/Cu(111) electronic moiré, the authors should provide more experimental evidence that this effect can be reproduced for different moiré periodicities.xiv) In Figure 4 the STS were performed at a DCA anthracene lobe position.This point is not mentioned in the manuscript and is important.For completeness, the authors should perform the gating experiment on a Cu adatom position.xv) Figure S10.It is not clear at all that the charging rings are increasing their perimeter around the DCA molecule (see ref. 31).It looks just the same intensity at the Cu positions.This is not consistent with the molecular charging ring features reported in ref. 31.These dI/dV maps do not support the interpretation of charging peaks given in Figure 4 of the manuscript.
Reviewer #2 (Remarks to the Author): In their manuscript entitled "Gate control of Mott metal-insulator transition in a 2D metal-organic framework", B. Lowe et al claim that in a metal-organic network grown on an hBN/Cu(111) substrate it is possible to control a metal-insulator transition through two mechanisms.One of them is based in the modulation of the surface potential due to the presence of a moiré pattern between hBN and Cu(111).In the second part of the manuscript, they control the transition by varying the sample tip distance.There are different aspects of the article that need to be clarified before the article can be published.
Figure 3 shows the spectra measured by moving the tip between the areas of the moiré called pores to the areas called wires.The experimental spectra show a modulation in the position of the bands depending on the moiré area.Upon reaching the areas called wires, the gap disappears and very intense peaks extend from the Fermi level up to +0.4eV.These spectra features are not mentioned or discussed in the manuscript.
The calculations reproduce the energy position of the bands observed in the experiment until the wire areas where the disagreement with the experiments it is clear.The calculations corresponding to the wire areas show very pronounced and very narrow peaks.The authors attributed their origin to coherent quasiparticle.Contrary to what the authors say in the manuscript, the calculations do not show a gap collapse in the wire areas, on the contrary it becomes wider and extends to almost +0.4eV.
According to the authors, the control of the metal-semiconductor transition induced by the substrate is deduced from the comparison between the experimental results and the theoretical calculations shown in Figure 3. Before this can be stated it is necessary to discuss in detail the discrepancies mentioned above between theory and experiments.
In the second part, the authors show how the metal-insulator transition can be induced by changing the tip-sample distance.To do this, they carry out experiments in one of the areas called wire. Figure 4d shows how in this area the measured spectra may or may not show a gap depending on the tipsample distance.This result somehow invalidates the manuscript's first claim that moiré registration controls the existence of a gap or not.It seems that the gap collapse depends on the parameters used to perform the measurements.
After reading the manuscript and the supplementary material, it is not clear to me how the assignments of the purple circles and red squares are made in Figure 4 or how it is decided whether the observed gap corresponds to a trivial insulator or a Mott insulator.
No details are given as to whether the energy levels shown in Figure S12 are a cartoon or the result of a calculation.This detail is important to understand how the authors identify the gap character.
Reviewer #3 (Remarks to the Author): In this work, the authors reported the experimental synthesis and characterization of a single-layer 2D DCA3Cu2 MOF on a wide bandgap BN substrate, which is further shown to host a robust Mott insulating phase and can achieve a Mott metal-insulator transition using electrostatic control.The experimental observations are quantitatively consistent with theoretical predictions (both DMFT calculations and DBTJ model).Direct experimental measurements on a Mott metal-insulator transition in 2D MOFs remain elusive.One of the challenges lies in the experimental synthesis of large single-crystal MOF samples.It is nice to see that the authors have succeeded in making one such sample and successfully demonstrated the Mott metal-insulator transitions induced via either template or tip.However, it is important for the authors to address a question that arises from the examination of the large-scale samples, as depicted in Figures 1a and S4.One can clearly see structural defects, such as vacancies and grain boundaries.As these defects may have a profound influence on the electronic properties of the MOF, it would be good for the authors to have some discussion about the potential impact of these bulk defects.This work represents a noteworthy contribution to the research field of 2D MOFs, shedding light on elucidating the Mott metal-insulator transition in MOFs.I would recommend its publication in Nature Communications after the authors address the aforementioned concerns.

Reviewer 1
B. Lowe et al. report on the DCA3Cu2 2D MOF fabrication (following the concepts of supramolecular coordination chemistry) on h-BN/Cu(111) under ultra-high vacuum (UHV).Its structural and electronic properties are studied by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), supported with density functional theory (DFT) and dynamical mean-field theory (DMFT) calculations.The combination of the wide bandgap h-BN as a template (allowing the 2D-MOF to retain its intrinsic electronic properties), and of the adequate energy level alignment given by the h-BN/Cu(111) substrate (resulting in half-filling of the 2D-MOF kagome bands) promotes the realization of a correlated-electron Mott phase.With STS measurements, they find an electronic energy gap of around 200meV, corresponding to a Mott insulating phase according to DMFT predictions.In addition, by tuning the electron population of the 2D-MOF near-Fermi band structure, via either template induced (work function variation of the pores and wires of the h-BN/Cu(111) electronic moiré) or tip-induced gating (via STM probe sample distance) a Mott metal-insulator transition in the 2D-MOF is proposed.
Even though this work claims the observation of an exotic many-body quantum phenomenon (Mott metal-insulator transition) in a 2D-MOF, the experimental evidence and theoretical support are not strong enough.Therefore, the status of this work is still too preliminary so that it can be published in Nature Communications.The Mott metal-insulator transition should be present in the entire 2D-MOF material (since this effect alters the band structure of the material).Therefore, the present claim that this effect can happen at the local scale (< 5 nm) sounds controversial.

Author reply:
Our dI/dV STS measurements show that: (i) the 2D kagome MOF exhibits an electronic energy gap of ~200 meV (Fig. 2), with occupied and unoccupied band edges following a spatial modulation (from pore to wire regions) given by local variations of the work function resulting from the hBN/Cu(111) moiré pattern (Fig. 3); (ii) when the STM tip is far enough from the surface (such as to not significantly shift the MOF energy levels via the doublebarrier tunnelling junction effect), the entire 2D kagome MOF is in a Mott insulating phase, with Mott insulating energy gaps both at the pore and wire regions of the hBN/Cu(111) moiré pattern Fig. 4 and SI Fig. S4); (iii) for smaller tip-sample distances, the wire region exhibits a metallic dI/dV spectrum, with no energy gap and a significant dI/dV signal at the Fermi level, while the pore regions remain Mott insulating (Fig. 3b).We interpret these experimental observationswhich are reproduced by our DMFT calculationsas a transition at the wire regions from a Mott insulating phase to a metallic phase; this transition results from the depletion of the kagome MOF electronic bands due to the combination of: (i) large local work function at the wire region (Fig. 3c), and (ii) tip-induced MOF energy level shifts due to the double-barrier tunnelling junction (Fig. 4).
In the Mott insulating phase (i.e., moiré pore regions, and moiré wire regions for large tipsample distances), electronic states are intrinsically localised at kagome lattice sites due to strong on-site Coulomb repulsion, with an electronic mean free path that is smaller than the MOF lattice constant.That is, the concept of band structure within conventional band theory (i.e., eigenenergies of single-electron wavefunctions as a function of single-electron wavefunction wavevector k) can be ill defined, with near-Fermi Hubbard 'bands' that can be incoherent, and electronic phenomena are fundamentally local.Now, at moiré wire regions, when the tip-sample distance is reduced (Fig. 4), we claim that the combined effects of local work function (larger than for the moiré pore regions; Fig. 3c) and double-barrier tunnelling junction lead to a depletion of the localised electronic states of the MOF in the Mott insulating phase (i.e., effectively, a lowering of the MOF chemical potential), within the area of the tunnelling junction (with a typical characteristic length scale of ~10 nm given by the tip radius of curvature).This depletion of electronic states leads to the collapse of the Mott insulating phase, into a metallic phase with no gap and an increased density of states at the Fermi level (Fig. 3b, e-g, and Fig. 4d).We acknowledge that this effect occurs within an effective area defined by the tunnelling junction cross section (i.e., typically ~10 nm in length), and that electronic confinement at such moiré wire regions can lead to features in the local density of states that are not captured quantitatively by our DMFT calculations.
It is important to note that Mott insulating phases have been observed recently in monolayer 1T-TaS2 and 1T-TaSe2, which are 2D crystals with an hexagonal Bravais lattice and a lattice constant of ~2 nm, within crystalline domains with characteristic length scales of ~10 nm. 1,2 Importantly, 1T-TaS2 domains with characteristic length scales of ~5 nm can be metallic (i.e., ungapped and with a non-zero density of states at the Fermi level) when strained. 3These phenomena are very similar to the case of our 2D MOF here, and support our interpretation of a Mott insulating phase in monolayer domains with characteristic length scales of ~5-10 nm, with possible local transitions to a metallic phase.
We have now clarified this in our main text discussion (before the conclusion).Our work is not preliminary; it provides a complete characterisation, description and interpretation of our experimental observations, supported by a theoretical formalism (DMFT) which depicts correlated-electron phenomena accurately and reliably (in contrast with other formalisms such as DFT). 4-6  Additional experimental evidence, such as temperature dependence studies of the insulating gap size and angle-resolved photoemission spectroscopy measurements are necessary.
Following this suggestion from Reviewer 1, we have now performed dI/dV STS measurements at DCA anthracene extremity sites of the 2D kagome MOF at 77 K, at pore and wire regions of the hBN/Cu(111) moiré pattern (with moiré periodicity similar to the moiré domain in the main text; see below and new Supplementary Fig. S31a).These measurements at 77 K reveal a ~200 meV electronic gap at pore regions, and no gap at the Fermi level and an increased Fermi-level dI/dV signal for wire regions (for an intermediate tip-sample distance, as for Fig. 3b in main text), similar to what we observed at 4 K (with some trivial thermal broadening).We also performed further DMFT calculations (U = 0.65 eV) of the spectral function, for chemical potentials EF = 0.4 eV (Mott insulating phase) and EF = 0.2 eV (metal-like phase with no gap at the Fermi level), for temperatures between 29 and ~600 K (see below and new Supplementary Fig. S32).These DMFT-calculated spectral functions show no significant changes as the temperature varies within this range (except for trivial thermal broadening), in very good agreement with experiments.Importantly, these supplementary measurements and calculations indicate that: (i) the Mott insulating gap is robust up to high temperatures (in particular room temperature), and (ii) changes in dI/dV spectra are likely to become significant only for temperatures well above room temperature, at which STS measurements are challenging if not possible.We have now added a new Supplementary Section S23 on this matter.
Reviewer 1 also suggests that angle-resolved photoemission spectroscopy (ARPES) measurements might be useful for supporting our claims.We agree that ARPES might be useful as a complementary technique in future studies on systems similar to the one we focus on here.However, ARPES is not adequate for the specific system that we consider here, a single-layer 2D MOF adsorbed on an atomically thin 2D insulator.ARPES does not allow for the detection of unoccupied states (useful for the observation of the Mott insulating energy gap).For our particular sample, k-resolution would be impossible due to the different rotational orientations of the hBN domains on Cu(111), which give rise to different moiré patterns (i.e., there would be multiple crystalline domains within the spot size of an UV light/X-ray source).Moreover, ARPES could lead to radiation-induced damage of the material of interest (in particular of compounds composed of organic molecules as here).In our present case, where the MOF is adsorbed on insulating hBN, irradiation by UV light/Xrays is likely to result in charging (unless an electron flood gun is used), imposing further challenges on ARPES measurements.Importantly, conventional ARPESa space-averaging techniquecannot provide the real-space resolution necessary for distinguishing MOF electronic properties at pore and wire regions of the hBN/Cu(111) moiré pattern (due to the large UV/X-ray spot size).It would also not allow for measuring MOF energy level shifts via the double-barrier tunnelling junction (DBTJ) effect (for which the STM tip is required), which drive the transitions from Mott insulator to metal at the wire regions.It is well established that Mott energy gaps and Mott insulating phasesincluding gate-controlled transitions to metallic phases -can be evidenced via dI/dV STS, without the need of ARPES. 1,3,7-9Low-temperature dI/dV STS provides very good energy resolution, capability for detecting both occupied and unoccupied states non-invasively, and real-space atomicscale resolution (useful here for distinguishing MOF electronic properties at wire and pore regions of the hBN/Cu(111) moiré pattern).In addition, the authors should carefully address the following major concerns that I have (points i to xv).
i) The DCA3Cu2 2D-MOF has already been studied on a decoupling layer such as graphene (ref.31).There a long-range ordered 2D-MOF phase was achieved, by far exceeding the quality of the DCA3Cu2 2D-MOF presented in this manuscript.Even though the authors claim to have achieved a highly crystalline growth, this is not the case so far.The authors must provide better experimental proof to defend this point.
The DCA3Cu2 2D MOF has indeed been studied on graphene before, as acknowledged and referenced explicitly (previous Ref. 31;updated Ref. 33) in our manuscript. 10This previous study is however fundamentally different from ours: graphene is a semimetal with no energy gap, whose electronic states hybridise with those of the 2D DCA3Cu2 MOF (see Fig. 3b

image in the Supplementary Information (SI) with a large amount of presumably unreacted Cu on the surface (bright features in figure below, which the authors fail to explicitly comment on) and with clear domain boundaries. Note that the colour scale and resolution of this latter ~150x150nm 2 image hinder a reliable evaluation of the overall homogeneity or possible defects of the MOF. Moreover, no Fourier transforms (FTs) of these MOF domain STM images are provided, making a comparison of crystallinity impossible.
Synthesising a large single-crystal MOF is challenging.Here we succeeded in synthesising 2D MOF domains with characteristic lengths of several tens of nm's, with very good quality in terms of monocrystallinity and defect density.This is evidenced by our large-scale STM images (60x60nm 2 in Fig. 1a, 300x300nm 2 in SI Fig. S7, and 100x100nm 2 in SI Fig. S8a), and, importantly, the FTs of these images, showing clear sharp diffraction peaks (inset in Fig. 1a; SI Fig. S8).Note that in our manuscript we explicitly acknowledge the presence of DCA-only domains, and that in the SI we explain that we sacrifice some of the overall MOF yield to obtain high-crystallinity of the MOF domains.
Previous STM and dI/dV STS studies on 2D materials with a lattice geometry similar to that of our MOF here (e.g., single-layer 1T-TaS2, with a 2D hexagonal lattice and a lattice constant on the order of ~2 nm) have shown a Mott insulating phase on nanoisland domains with characteristic sizes on the order of ~10x10nm 2 . 1 That is, our monocrystalline MOF domains with characteristic lengths on the order of several tens of nm's are sufficiently large to demonstrate a Mott insulating phase.
We have now updated our manuscript, nuancing our previous claim of "highly crystalline growth" and changing it to "monocrystalline growth of the MOF domains".We have now added comments to the main text discussing explicitly the presence of defects in our MOF domains and of DCA-only regions.We have also added a 300x300 nm 2 image (Fig. S7) to the Supplementary Section S6), highlighting the quality and homogeneity of the 2D MOF, and an SI section on how defects affect the MOF electronic properties (Supplementary Section S11).ii) The authors claim in the abstract that correlated-electron phases, or 2D-MOF "quantum materials" have not been experimentally realized yet.However, in a recent paper, already uploaded into arXiv before this manuscript, Lobo-Checa et al. report 2D magnetism in a very similar 2D-MOF i.e., the DCA3Fe2 2D-MOF grown on Au(111) (see https://arxiv.org/abs/2209.14994).The authors should give credit to other colleagues working in the same research field.This preprint should be mentioned in the introduction and cited.

We thank Reviewer 1 for drawing our attention to this relevant reference. We have now added it to the introduction as requested (updated Ref. 26). We acknowledge that Lobo-Checa et al. have reported ferromagnetism in the DCA3Fe2 MOF, as the result of exchange interactions (i.e., correlations) between unpaired
Fe 3d electrons across the organic DCA linkers. 11The main message and physics reported in our manuscript are, however, fundamentally different: the Mott insulating phase results from strong Coulomb interactions between electrons populating the DCA3Cu2 MOF near-Fermi kagome bands, which have dominant DCA molecular orbital character, with the Cu 3d shell completely filled (see Kumar et al. DOI: 10.1002/adfm.202106474;updated Ref. 25 in our manuscript) 12 .We have now tried to emphasise and clarify this throughout the manuscript.
iii) The synthesis of a 2D-MOF on h-BN via supramolecular coordination chemistry is not new (see ref.30).In addition, the gate control of the DCA3Cu2 2D-MOF electronic structures and charging was also already performed on graphene (ref.

31).
We agree with both Reviewer comments.We do not intend to claim otherwise on either point.We explicitly acknowledge that growth of a 2D MOF (with square lattice) on hBN 13,14  (previous Ref. 30; updated Refs.31, 32; updated line 95 of main text), as well as tip-induced gating (i.e., charging via the double-barrier tunnelling junction effect; see Fig. 4a, b in old Ref. 31,now ref. 33; line 247) of unoccupied molecular orbitals of the same DCA3Cu2 MOF on graphene, have been achieved previously. 10  We do emphasise, however, that our work represents the first experimental demonstration of: (i) growth of a single-layer 2D MOF with kagome crystal structure on an atomically thin wide bandgap 2D insulator, and (ii) electrostatic control over a Mott insulating phase therein.These findings are fundamentally different from those reported in old Refs.30, 31.iv) page 3 (lines 84-85) "a crystalline MOF domain" growth is claimed.However, compared to ref. 31, this is far from crystalline.As shown in Fig. 1(a) of the manuscript, the MOF domain is surrounded by excess DCA molecules, therefore the 3:2 stoichiometry was only successfully achieved on rather small regions of the sample (50 × 50 nm2).In addition, white islands embedded into the 2D-MOF domains may point out to excess Cu islands.Can the authors identify such islands?There are also many additional defects in the MOF domain which are not discussed (black or dark blue points, wires or regions inside the domain).It is therefore almost impossible to find more than two h-BN pore regions together, covered by defect free DCA3Cu2 2D-MOF.The authors should provide experimental evidence of a long-range ordered growth of the 2D MOF.Otherwise, the authors should discuss the defects appearing in the 2D-MOF domains, as well as their limitations to achieve a highly crystalline 2D-MOF growth.This is an important point since such small domain sizes and high defect density will preclude the use of such 2D-MOFs in electronic devices.

As outlined in our response to point i) above, we dispute the Reviewer's assessment of the comparison of the DCA3Cu2 MOF crystallinity between our manuscript here and previous Ref. 31 (updated Ref. 33). Previous Ref. 31 (updated Ref. 33) by Yan et al. provides two large-scale STM images of the DCA3Cu2 MOF on graphene: a ~40x40nm 2 image in the main text of a MOF region showing good crystallinity but which is not defect-free [see Fig. provided in answer to point i)], and a ~150x150nm 2 image in the SI with a large amount of presumably unreacted Cu on the surface [bright features in panel b of Fig. above in point i),
which the authors fail to explicitly comment on] and with clear domain boundaries. 10No Fourier transforms (FTs) of these MOF domain STM images are provided, making a comparison of crystallinity difficult.
We succeeded in synthesising 2D MOF domains with characteristic lengths of several tens of nm's, with very good quality in terms of monocrystallinity and defect density.This is evidenced by our large-scale STM images (60x60nm 2 in Fig. 1a and 100x100nm 2 in Supplementary Fig S8a), and, importantly, the FTs of these images, showing clear sharp diffraction peaks (inset in Fig. 1a of our manuscript; SI Fig. S8b, c).In our manuscript we explicitly acknowledge the presence of DCA-only domains in these images, and in the SI we explain that we sacrifice some of the overall MOF yield to obtain crystalline MOF domains.
We have now updated our manuscript, nuancing our previous claim of "highly crystalline growth" and changing it to "monocrystalline growth of the MOF domains".We have now added comments to the main text discussing explicitly the presence of defects in our MOF domains and of DCA-only regions.In the SI, we have also added a Supplementary Section S11 on how such defects might affect the MOF electronic properties, as requested by Reviewer 1.
We have also added a 300x300 nm 2 image of the DCA3Cu2 MOF on hBN/Cu(111) to the Supplementary Section S6 (see Fig. S7).In this image, no DCA-only domains are observed, indicating that the DCA-to-Cu stoichiometry is close to 3-to-2 for this sample preparation (with some Cu clusters, similar to previous Ref. 31  We emphasise that the main findings of our manuscript are: (i) the observation of a significant Mott gap in a single-layer 2D kagome MOF grown on an atomically thin insulator, and (ii) the potential for controlling such Mott gap and insulating phase electrostatically.As mentioned above, previous STM and dI/dV STS studies on 2D materials with a lattice geometry similar to that of our MOF here (e.g., single-layer 1T-TaS2, with a 2D hexagonal lattice and a lattice constant of ~2 nm, similar to our system) have shown a Mott insulating phase on nanoisland domains with characteristic sizes on the order of ~10x10nm 2 (see updated Ref. 49  2 , is beyond the scope of our current manuscript and requires further studies.v) page 4 (line 87).Here the growth of the 2D-MOF on top of the h-BN/Cu(111) electronic moiré is presented.However, it is known that the moiré periodicity can change approximately from 3 nm to 14 nm on the h-BN/Cu(111) samples grown with borazine in UHV (ref.30).Is there any moiré periodicity preference for the successful growth of 2D-MOF islands on top?The authors should provide a discussion in this regard.

in main text by Vano et al.). That is, our monocrystalline MOF domains with characteristic lengths on the order of several tens of nm's are sufficiently large to support these findings. The growth of a perfectly crystalline monolayer 2D kagome MOFs on an atomically flat insulator, across areas significantly larger than ~100x100nm
We thank Reviewer 1 for this valid comment.In our manuscript we focus on the DCA3Cu2 MOF grown on hBN/Cu(111) moiré domains with periodicities of ~10-12 nm, since these hBN/Cu(111) regions seem to be the most commonly formed.We do observe examples where the 2D MOF grows on rarer hBN/Cu(111) domains with smaller moiré periodicity (e.g., ~5 nm), where the 2D MOF shows structural and electronic properties similar to those on hBN/Cu(111) moiré domains with a ~10 -12 nm periodicity, with dI/dV spectra that are consistent with our physical interpretation.
We believe the MOF has no growth preference for particular moiré pattern periodicities.Establishing whether the 2D MOF growth quality depends on the hBN/Cu(111) moiré periodicity is, however, beyond the scope of this manuscript and requires further investigations.
We have now added a comment on this matter in Supplementary Section S6, and a new Supplementary Section S15 including data on the electronic properties of the MOF on hBN/Cu(111) domains with moiré periodicities of ~5 nm and ~10 nm.We have now included an explicit mention of the growth of the DCA3Cu2 MOF on graphene/Ir(111) on p. 4, lines 102-103, citing previous Ref. 31 (updated Ref. 33), as requested by Reviewer 1.We do emphasise that the findings of our work are fundamentally different to those of (previous) Ref. 31 by Yan al. 10 The electronic states of graphenea semimetal with no energy gap and with significant electrical conductivitydo show some degree of hybridisation with those of the DCA3Cu2 2D MOF (see Fig. 3b 1d). 14We therefore think our growth upon an insulating hBN layer represents a significant advancement towards potential technological applications.
vii) With respect to Figure 1.The authors only focus on the kagome band structure close to the Fermi level.However, it is known that more kagome bands should appear above and below the energy range considered here (ref.19).Can the authors comment on this point?Do the authors have DFT calculations for a wider energy range?How does the band structure of the Mott insulating phase look like?
We have added a plot of our DFT calculations for a wider energy range (-3 to 3 eV), for both the free-standing MOF and the MOF on hBN/Cu(111) (see below and new Supplementary Section S1).These calculations, in good agreement with Ref. 19 in the main text, show the three kagome bands near the Fermi level separated from lower-lying occupied and upperlying empty bands by >1.5 eV.Note that DFT tends to underestimate energy gaps, so this energy separation could be even larger.Because this energy separation is so large, the essential correlated-electron physics can be described by considering solely electronic states near the Fermi level.More DFT calculations can also be found in our previous publication. 15  We have also added to the SI a plot of the energy-and wavevector-dependent spectral function, A(E, k), for the Mott insulating phase, calculated via DMFT (U = 65 eV; EF = 0.4 eV, i.e., near half-filling; new Supplementary Section S5).This spectral function shows a significant gap at the Fermi level, with an occupied lower Hubbard band with weakly dispersive features (in particular close to the Γ point), and an empty upper Hubbard band (UHB) with significantly less dispersion.Notably, the diffuse nature of these bands (as opposed to sharp and well-defined, as in conventional band theory) is indicative of band incoherence; this is expected for a Mott insulating phase.
It is important to note that, as mentioned in the main text (lines 125 -126, p. 5), DMFT captures many-body effects more accurately and reliably than DFT.As such, DMFT is a valid approach for determining the electronic structure of the Mott insulating phase in our case here, and of strongly correlated materials in general. 4 As requested by Reviewer 1, we have now added a new Supplementary Section S12 with a dI/dV spectrum at a MOF DCA lobe site, at a hBN/Cu(111) moiré pore region, on a larger voltage range, from -1 to +1 V (see below).Such a spectrum shows no clear prominent electronic features (e.g., HOMO/LUMO signatures) outside the -0.5 to +0.5 V energy range reported in the main text.This is consistent with our DFT calculations (see above; Supplementary Fig. S1) and those of Ref. 19, which show three kagome bands with dominant DCA LUMO character near the Fermi level, well separated in energy from other fully occupied and completely empty bands lying beyond ~1.5 eV below and above the Fermi level, respectively.This is the reason why in our manuscript we focus on the -0.5 to 0.5 V bias voltage range.Note that performing dI/dV STS within a large bias voltage range (e.g., -2 to 2 V) is not trivial due to challenges in preparing a spectroscopically functional STM tip on the MOF/hBN/Cu(111) system.
We have now added A. Kumar et al. Nano Letters 18, 5596 (2018) as a reference (new Ref. 52 in main text), as requested by Reviewer 1. 16 Note that the (non-interacting) band structure of DCA3Co2 on graphene is fundamentally different from that of DCA3Cu2 on hBN, with the former hosting multiple bands near the Fermi level with very significant contributions from Co states [e.g., see Fig. 4b of Kumar et al. Nano Letters 18, 5596 (2018)]. 16The DCA3Cu2/Cu(111) system of (old) Ref. 33 (new Ref. 35) is also fundamentally different from our DCA3Cu2/hBN/Cu(111) system, with the MOF interacting significantly with the underlying, more reactive Cu(111) substrate, with significant hybridization between MOF and Cu(111) states, and the near-Fermi kagome bands not half-occupied [see B. Field et al., npj Computational Materials 8, 227 (2022)]. 15,17We therefore assert that a quantitative comparison between the electronic properties of our DCA3Cu2/hBN/Cu(111) system, and those of DCA3Cu2/graphene and DCA3Cu2Cu(111), is not meaningful.ix) page 6 (line 149) "the high crystalline growth makes a large disorder-related gap unlikely".If this is the case, how does the STS look at different points of the 2D-MOF island?Are the features identical if one performs STS on the dark pore regions?How do the electronic properties look like at the edge of the 2D-MOF domain?At which position does the domain edge already play a role in disturbing the reported electronic properties?
We thank Reviewer 1 for these valid comments.We have now provided further dI/dV STS measurements at the high-symmetry MOF locations: Cu, DCA lobe, DCA centre and MOF pore sites (to not confuse with what we refer to as a hBN/Cu(111) moiré pore region); see new Supplementary Section S10.The dI/dV spectra at DCA centre and dark MOF pore sites are qualitatively similar to the spectra at adjacent Cu and DCA lobe sites, with spectral features (i.e., lower and upper Hubbard bands) at these Cu and DCA lobe sites stronger.This is consistent with the STM images and dI/dV maps taken at bias voltages corresponding to the lower Hubbard band maximum and upper Hubbard band minimum (see Supplementary Figs.S11-12), showing higher intensity at Cu and DCA lobe sites.
We also added a new Supplementary Section S24 where we compare dI/dV spectra acquired at different pore regions of a hBN/Cu(111) domain with a moiré period of λ ≈ 12.5 nm.The spectra in Supplementary Fig. S23 are very consistent across six distinct moiré pores.This shows that within the bulk of a MOF domain, the MOF local electronic properties are identical for equivalent sites with respect to the hBN/Cu(111) moiré pattern.
We have also added a new Supplementary Section S11 where we explore the effect of defects (e.g., MOF domain edges and boundaries, vacancies, cracks) on the MOF electronic properties.Supplementary Fig. S14   18 Notably, one unit cell away from the MOF domain edge, the MOF local electronic properties are identical to those within the MOF domain bulk.
We have also performed additional dI/dV STS measurements at a defective MOF domain boundary (new Supplementary Fig. S15), qualitatively consistent with dI/dV spectra at the MOF domain edge.Similarly, no significant disturbance in MOF electronic properties is found at defective Cu vacancy sites (new Supplementary Fig. S16).This is not consistent with the molecular charging ring features reported in ref. 31.These dI/dV maps do not support the interpretation of charging peaks given in Figure 4 of the manuscript.

Reviewer 2
In their manuscript entitled "Gate control of Mott metal-insulator transition in a 2D metalorganic framework", B. Lowe et al claim that in a metal-organic network grown on an hBN/Cu(111) substrate it is possible to control a metal-insulator transition through two mechanisms.One of them is based in the modulation of the surface potential due to the presence of a moiré pattern between hBN and Cu(111).In the second part of the manuscript, they control the transition by varying the sample tip distance.There are different aspects of the article that need to be clarified before the article can be published.
Figure 3 shows the spectra measured by moving the tip between the areas of the moiré called pores to the areas called wires.The experimental spectra show a modulation in the position of the bands depending on the moiré area.Upon reaching the areas called wires, the gap disappears and very intense peaks extend from the Fermi level up to +0.4eV.These spectra features are not mentioned or discussed in the manuscript.
We thank Reviewer 2 for this valid comment.Indeed, the experimental dI/dV spectra in Fig. 3b for locations near the hBN/Cu(111) moiré wire region show significant peaks between the Fermi level and Vb ~0.4 V.At such locations close to the wire regions, we observed dI/dV features due to tip-induced charging via the double-barrier tunnelling junction (DBTJ) effect; see Fig. 4. We therefore propose that these dI/dV peaks in Fig. 3b could be the result of tipinduced charging via the DBTJ effect, as observed for moiré wire regions and described in Fig. 4. Note that the DMFT calculations do not consider the DBTJ or tip-induced effects; therefore, they cannot predict such features.We have now added a paragraph on this matter in the main text, and a related new Supplementary Section S17.
We want to emphasise that the main messages of our manuscript are: (i) the observation of a significant Mott gap in a single-layer 2D MOF, and (ii) the electrostatic control of such Mott gap and insulating phase.As such, in the main text we focus on dI/dV features at energies close to the Fermi level.The calculations reproduce the energy position of the bands observed in the experiment until the wire areas where the disagreement with the experiments it is clear.The calculations corresponding to the wire areas show very pronounced and very narrow peaks.The authors attributed their origin to coherent quasiparticle.Contrary to what the authors say in the manuscript, the calculations do not show a gap collapse in the wire areas, on the contrary it becomes wider and extends to almost +0.4eV.According to the authors, the control of the metal-semiconductor transition induced by the substrate is deduced from the comparison between the experimental results and the theoretical calculations shown in Figure 3. Before this can be stated it is necessary to discuss in detail the discrepancies mentioned above between theory and experiments.
We thank Reviewer 2 for these very valid comments, with which we agree.Indeed, in the main text (previously, p. 7, line 181), we claimed that the DMFT calculations show, for a chemical potential corresponding to the moiré wire region, a collapse of the energy gap Eg.What we meant is that, for such a chemical potential (i.e., smaller than that for a moiré pore region), the DMFT calculations show no gap at the Fermi level, with a non-zero increased spectral function (indicating the presence of electronic states) at the Fermi level.This is consistent with our experiments, which show a larger Fermi-level dI/dV signal at the moiré wire region in comparison to the moiré pore region (for the considered tunnelling conditions; see updated Fig. 3e and new Supplementary Sections S14-15), and with our claim of a metallic phase at the moiré wire region (i.e., for tunnelling parameters, in particular tipsample distance, used in Fig. 3).This increase in Fermi-level DMFT-calculated spectral function and measured dI/dV marks the onset of the Mott energy gap collapse, and of the transition from Mott insulating phase to metal (see Supplementary Fig. S2b).
As pointed out by Reviewer 2, the DMFT calculations for a chemical potential corresponding to the moiré wire region show a pronounced narrow peak near the Fermi level.These peaks are not observed in our experimental dI/dV curves (Fig. 3

We have now updated the main text, clarifying what we mean by 'gap collapse', and providing a more detailed discussion on the discrepancies between experiment and theory.
In the second part, the authors show how the metal-insulator transition can be induced by changing the tip-sample distance.To do this, they carry out experiments in one of the areas called wire. Figure 4d shows how in this area the measured spectra may or may not show a gap depending on the tip-sample distance.This result somehow invalidates the manuscript's first claim that moiré registration controls the existence of a gap or not.It seems that the gap collapse depends on the parameters used to perform the measurements.

We thank Reviewer 2 for this valid comment. We acknowledge that our main text was perhaps not perfectly clear on this point. Both the considered MOF region relative to the underlying hBN/Cu(111) moiré pattern and the tunnelling parameters (i.e., tip-sample distance, bias voltage) determine the energy level alignment and population of the MOF electronic states, and hence the corresponding electronic phase (i.e., Mott insulator or metal) of the MOF region at the STM junction.
It is important to note that: (i) the MOF at the hBN/Cu(111) moiré pore regions exhibits a Mott gap and is in the Mott insulating phase regardless of the tunnelling parameters, (ii) the MOF at the hBN/Cu(111) moiré wire regions exhibits a Mott gap and is in the Mott insulating phase for large tip-sample distances (i.

e., when MOF energy level shifts due to the double-barrier tunnelling junction are negligible), and (iii) the MOF at the hBN/Cu(111) moiré wire regions is in a metallic phase (with no energy gap at the Fermi level, and with a significant non-zero Fermi-level density of states) for intermediate tip-sample distances (i.e., when MOF energy level shifts due to the double-barrier tunnelling junction result in partial depopulation of MOF electronic states).
We have revised our main text to make this clear.
After reading the manuscript and the supplementary material, it is not clear to me how the assignments of the purple circles and red squares are made in Figure 4 or how it is decided whether the observed gap corresponds to a trivial insulator or a Mott insulator.
We thank Reviewer 2 for this valid comment.We agree that the explanation for the assignments of the purple and red markers, and of the observed gaps to a trivial or Mott insulator in Fig. 4, could be clearer in our manuscript.
The dI/dV spectra for the MOF at the hBN/Cu(111) moiré wire region in Fig. 4d show an electronic gap, with a clear peak (sharper than the near-Fermi band features in Fig. 3b, with a maximum indicated by the purple circles) at positive bias voltage for large tip-sample distances, and at negative bias voltage for small tip-sample distances.These spectra also show a subtler band edge (indicated by the red squares, similar to the near-Fermi band features in Fig. 3b; see updated Supplementary Section S8 for information on the determination of band edges) at a bias voltage of sign opposite to that of the sharp peak, i.e., at negative bias voltage for large tip-sample distances and at positive bias voltage for small tip-sample distances.For intermediate tip-sample distances, these spectra are gapless, with a significantly larger Fermi-level dI/dV signal (see Fig. 4f).From these observations, we infer that the MOF is an insulator (trivial or Mott) for large and small tip-sample distances (i.e., dI/dV spectra with a gap at the Fermi level), and a metal for intermediate tip-sample distances (i.e., dI/dV spectra with no gap at the Fermi level).

The bias voltage position of the sharp peak (purple circles) increases linearly with respect to tip-sample distance, whereas the bias voltage position of the subtler band edge decreases nonlinearly with tip-sample distance. Notably, Eqs. 1, 2 of the main text (now on p. 10), corresponding to the double-barrier tunnelling junction (DBTJ) model, provide very good fits for the bias voltage positions of both sharp peak and subtle band edge as a function of tipsample distance (black curves in
Fig. 4e).This provides compelling evidence that the sharp peaks (purple circles) are associated with charging of an intrinsic MOF electronic state lying at the edge (red squares) of a fully populated (large tip-sample distances) or completely empty (small tip-sample distances) band (see cartoon schematics in Fig. 4a-c and now Supplementary Fig. S26, and previous Refs. 33,43,45,now Refs. 33,46,48).Now, dI/dV spectra for the MOF at a pore region of the hBN/Cu(111) moiré pattern show a ~200 meV electronic energy gap at the Fermi level (Fig. 2).These spectra resemble the spectral function of the 2D kagome MOF in the Mott insulating phase (Fig. 1e), calculated via DMFT with a chemical potential that is consistent with the DFT-predicted occupation of the near-Fermi kagome bands for the MOF on hBN/Cu(111) (Fig. 1d, Supplementary Fig. S1).At an adjacent moiré wire region, the local work function increases by ~0.2 eV for the specific periodicity of the MOF/hBN/Cu(111) domain considered (Fig. 3c; see new Ref.[29][30][31].Accordingly, the near-Fermi electronic states of the MOF at this moiré wire region are shifted upwards in energy in comparison to the near-Fermi electronic states of the MOF at the moiré pore region.The dI/dV spectra in Fig. 3b for this moiré wire region (for the specific tunnelling parameters used) show no gap at the Fermi level, with a significant nonzero Fermi-level dI/dV signal (new Fig. 3e; Supplementary Fig. S19), indicative of a metallic phase.These experimental dI/dV spectra are consistent with the spectral function of the MOF calculated via DMFT for a chemical potential that is reduced (in comparison with the DMFT calculations for the moiré pore region); such DMFT spectral function exhibits a significant magnitude and no gap at the Fermi level, indicating a metallic phase, resulting from the depopulation of the MOF bands (Fig. 3d and Supplementary Fig. S2).
From these observations we infer that: (i) the MOF at the moiré pore region is in a Mott insulating phase, and (ii) the MOF at the adjacent moiré wire region, for the specific tunnelling parameters used (i.e., bias voltage, tip-sample distance) in Fig. 3b, is in a metallic phase (as the result of the depopulation of the MOF near-Fermi electronic states due to the increase in local work function).

Now, let us consider the MOF at such a moiré wire region, which is in the metallic phase (i.e., for specific tunnelling parameters). The work function of the STM tip is larger than that of the sample (Supplementary Section S19). When the tip-sample distance is reduced, the double-barrier tunnelling junction (DBTJ) leads to an upward energy shift of the MOF electronic states [with respect to the Cu(111)
Fermi level]: the MOF electronic states become further depopulated (Supplementary Fig. S26).That is, when the dI/dV spectra in Fig. 4d transition from gapless (metallic) to gapped (insulator) as the tip-sample distance decreases, we infer that the MOF electronic states associated with the MOF kagome bands become empty, with the Fermi level lying below the bottom of the three kagome bands (see DFT band structure over a wide energy range in new Supplementary Fig. S1).From this, we associate the gapped dI/dV spectra at the top of Fig. 4d (for small tip-sample distances) to a trivial insulating phase of the MOF.
Let us again consider the MOF in the metallic phase at such a moiré wire region (i.e., gapless spectra in Fig. 4d

at intermediate tip-sample distances). When the tip-sample distance is now increased, the DBTJ leads to a downward energy shift of MOF electronic states [with respect to the Cu(111)
Fermi level], which become further populated (Supplementary Fig. S26).That is, when the dI/dV spectra in Fig. 4d transition from gapless (metallic) to gapped (insulator) as the tip-sample distance increases, we infer that the population of the MOF electronic states associated with the MOF kagome bands also increases in turn, reaching a threshold that opens the Mott gap, with the Fermi lying in such Mott gap.This population of MOF states (here driven by the DBTJ effect and the increase in tip-sample distance) is analogous to the population of MOF states at the adjacent moiré pore region (due to the smaller local work function at such a moiré pore region; Fig. 3c).From this, we associate the gapped dI/dV spectra at the bottom of Fig. 4d (for large tip-sample distances) to the Mott insulating phase of the MOF.This inference of a Mott gap at the moiré wire region for large tip-sample distances is supported by DMFT.Indeed, when the chemical potentials used in the DMFT calculations of Fig. 3d are all offset upwards by 45 meV (i.e., leading to further population of the MOF electronic states, mimicking the effect of a tip-sample distance increase), the metallic spectral functions associated with the moiré wire region (with no gap at the Fermi level) all become Mott gapped (see Supplementary Fig. S4).
We have now revised the main text and Supplementary Section S19, including details on how the purple circles and red squares in Fig. 4 were assigned, and on how we associated the observed energy gaps to either a trivial or Mott insulator.
No details are given as to whether the energy levels shown in Figure S12 are a cartoon or the result of a calculation.This detail is important to understand how the authors identify the gap character.
We thank Reviewer 2 for this comment.The schematics in Fig. 4a-c and in previous Supplementary Fig. S12 (now Supplementary Fig. S26) are qualitative, cartoon illustrations of the MOF energy level shifts that result from tip-sample distance variations and the doublebarrier tunnelling junction (DBTJ) effect.
We have now clarified this in the captions of Fig. 4a-c, methods section, and Supplementary Fig. S12 (now Supplementary Fig. S26).

Reviewer 3
In this work, the authors reported the experimental synthesis and characterization of a singlelayer 2D DCA3Cu2 MOF on a wide bandgap BN substrate, which is further shown to host a robust Mott insulating phase and can achieve a Mott metal-insulator transition using electrostatic control.The experimental observations are quantitatively consistent with theoretical predictions (both DMFT calculations and DBTJ model).Direct experimental measurements on a Mott metal-insulator transition in 2D MOFs remain elusive.One of the challenges lies in the experimental synthesis of large single-crystal MOF samples.It is nice to see that the authors have succeeded in making one such sample and successfully demonstrated the Mott metal-insulator transitions induced via either template or tip.
We thank Reviewer 3 for their comment and careful reading of our manuscript.However, it is important for the authors to address a question that arises from the examination of the large-scale samples, as depicted in Figures 1a and S4.One can clearly see structural defects, such as vacancies and grain boundaries.As these defects may have a profound influence on the electronic properties of the MOF, it would be good for the authors to have some discussion about the potential impact of these bulk defects.This work represents a noteworthy contribution to the research field of 2D MOFs, shedding light on elucidating the Mott metal-insulator transition in MOFs.I would recommend its publication in Nature Communications after the authors address the aforementioned concerns.We thank Reviewer 3 for this valid suggestion which has helped improve our manuscript.We have added a comment in the main text and a new Supplementary Section S11 focussed on the electronic properties of the MOF at defect sites (e.g.vacancies, domain grain boundaries) and at boundaries of 2D MOF domains.At these sites, dI/dV spectra show remnants of the Hubbard bands, with a weaker upper Hubbard band and an additional peak at ~0. 6   18 The influence of these defects on the MOF electronic properties is very local, however: a short distance away (~one MOF unit cell) from one of such defect sites or domain boundaries, the local MOF electronic properties are identical to those within a defect-free MOF bulk region (new Supplementary Figs.S14-16).We therefore claim that the presence of these defects does not alter the main message of our manuscript.I would like to thank the authors for their efforts in answering my questions, but I am afraid that the answers have not been convincing enough.
In the paper the authors say that they have produced a Mott insulator in a MOF layer.Experimentally, they observe a gap at the Fermi level, depending on the area of the sample (moiré) in which they make the measurements the gap moves in energy following the expected values for the surface potential (not measured) and in some areas the presence of the gap depends on the tip sample position.The assignment of the gap a Mott gap is based only on the DMFT calculations.The authors, in their response to the referees, acknowledge that the DMFT calculations are not capable of reproducing some of the experimental measurements due to limitations in the calculations.Some of the features not explained by the calculations are very prominent in the experiments.Due to these limitations, it seems to me that it is very risky to base the main finding of the article on theoretical calculation that only reproduces the experimental data partially and in some areas of the sample.
According to the authors "the DMFT calculations assume a uniform chemical potential for an infinite system, omitting effects of locality; this assumption is reasonable for the Mott insulating phase (i.e.localized states)".I think this assumption is wrong, the Mott insulator occurs because itinerant electrons are located by electronic correlations, so the calculation cannot be local, although the result is that the conduction electrons end up localized and prevented from moving.
Finally, I don't understand why the authors use the existence of DBTJ in some cases and not in others.The MOF is deposited in an insulator on Cu(111), and the MOFF presents a gap at the Fermi level, according to the authors a Mott gap, therefore I do not understand why in some cases it is considered that a DBJT exists and in other cases This is completely ignored without explanation.
Due to all the above, I cannot support the publication of the manuscript.
Reviewer #3 (Remarks to the Author): The authors have incorporated the suggested comments and made necessary modifications to the manuscript.Now, I recommend its publication.
In the paper the authors say that they have produced a Mott insulator in a MOF layer.Experimentally, they observe a gap at the Fermi level, depending on the area of the sample (moiré) in which they make the measurements the gap moves in energy following the expected values for the surface potential (not measured) and in some areas the presence of the gap depends on the tip sample position.The assignment of the gap a Mott gap is based only on the DMFT calculations.The authors, in their response to the referees, acknowledge that the DMFT calculations are not capable of reproducing some of the experimental measurements due to limitations in the calculations.Some of the features not explained by the calculations are very prominent in the experiments.Due to these limitations, it seems to me that it is very risky to base the main finding of the article on theoretical calculation that only reproduces the experimental data partially and in some areas of the sample It is well established that the kagome lattice can host a Mott insulating phase at half-filling if there is significant on-site Coulomb repulsion U (see Ref. 42 in main text).Furthermore, previous theoretical literature supports the existence of a large U and the emergence of a Mott insulating phase in the specific DCA3Cu2 MOF that we study here (see Refs. 27,36 in main text).Additionally, evidence of localised electrons as a result of a large U has already been demonstrated experimentally for this specific 2D MOF (Ref. 25).In this context, the claim of a Mott insulating phase is not controversial -especially given the strong agreement between experiment and dynamical mean-field theory (DMFT) calculations.DMFT is a wellestablished method for capturing effects of electronic correlations, faithfully describing the Mott metal-insulator transition 1-3 (see  in main text).
The agreement between experimental dI/dV spectra for the MOF at the moiré pore region and the DMFT spectral functions for the MOF in the Mott insulating phase is excellent, with quantitatively consistent spectral features, including: (i) spectral line shape with lower (LHB) and upper (UHB) Hubbard bands and a ~200 meV gap at the Fermi level, and (ii) energy modulation of the LHB and UHB due to electrostatic potential variations (in the experiment due to the local work function variation given by the hBN/Cu(111) moiré pattern, and in DMFT due to the variation of the chemical potential; Fig. 3b, d, f, g in main text).This energy modulation of the LHB and UHB is perfectly consistent with the moiré local work function variation, regardless of the hBN/Cu(111) moiré pattern periodicity (Supplementary Section S15).This moiré local work function variation of hBN/Cu(111), and its effect on the energy level alignment of atomic and molecular adsorbates, is very well established (44)(45)(46)(47).
This quantitative agreement provides compelling evidence that the DMFT calculations capture the fundamental electronic properties of the 2D DCA3Cu2 MOF at the hBN/Cu(111) moiré pore regions, and that the energy gap Eg = ~200 meV observed experimentally at the Fermi level for the MOF at these moiré pore regions can be attributed to a Mott insulating gap.As stated above, a Mott insulating phase for the kagome lattice and for the specific DCA3Cu2 MOF studied here is well supported by previous literature (Refs. 25,27,36,42 in main text).
The DMFT calculations also provide an explanation for the increase in Fermi-level dI/dV signal and absence of an energy gap at the Fermi level for the MOF at the moiré wire regions (for an intermediate tip-sample distance range), where the local work function is larger -and hence the population of the MOF electronic states can be reduced -in comparison with the moiré pore regions.Indeed, the DMFT calculations (main text Fig. 3d, Supplementary Fig. S2b) show that a reduction in the population of the MOF electronic states (i.e., reduction of the chemical potential) leads to a transition from the Mott insulating phase to a metallic phase, with an increase in Fermi-level spectral function and absence of a gap at the Fermi level.That is, the increase in Fermi-level dI/dV signal and absence of energy gap at the Fermi-level is indicative of a MOF metallic phase at the moiré wire regions (for a specific intermediate tipsample distance range), with electronic states that can be more delocalised than those of the MOF in the Mott insulating phase at the moiré pore regions.
We acknowledge that the effects of the long-range moiré electrostatic potential and of the finite double-barrier tunnel junction (DBTJ) cross section on these arguably delocalised metallic MOF states at moiré wire regions could result in dI/dV features that are not captured by the DMFT calculations (performed for a perfectly periodic, infinite, flat system).Further dI/dV features not captured by DMFT (e.g., dI/dV peaks at positive bias voltage in Figs.3b, 4d of main text and Supplementary Fig. S24) can also be explained by the susceptibility of tipinduced charging of MOF electronic states at (and in proximity of) the moiré wire regions due to the DBTJ effect.It is important to note that the DBTJ effect does manifest itself also in the moiré pore regions, similar to the moiré wire regions, also leading to energy shifts of the LHB maximum (LHBM) and UHB minimum (UHBM) as the tip-sample distance changes (Supplementary Sections 20, 21).However, given the smaller local work function in comparison to moiré wire regions (Fig. 3c in main text), the MOF energy gap at these moiré pore regions is centred with respect to the Fermi level (Fig. 3b, d in main text), with a significant energy difference between Fermi level and LHBM.This makes the Mott insulating phase at the moiré pore regions robust to energy level shifts given by tip-sample distance changes (within the range of tip-sample distances considered in our study), without tip-induced charging.These factors provide a plausible explanation of why experimental dI/dV spectra and DMFT spectral functions show some differences for the moiré wire regions.

It is important to note that calculations based on DMFT -or even on other theoretical formalisms that capture electron-electron interactions and many-body physics less accurately (e.g., DFT+U) -on systems with large unit cells [such as the moiré unit cell of our
DCA3Cu2/hBN/Cu(111) system studied here] are computationally challenging, if not intractable.Such calculations become even more complex or unfeasible if tip-induced effects are taken into account.Our work provides a tractable approach in which electronic correlations and many-body effects are accounted for reliably, with excellent agreement between experiment and theory for moiré pore regions, and good qualitative agreement for the near-Fermi spectral features at the moiré wire regions.We assert that these aspects provide sufficient evidence for: (i) a Mott insulating phase for the MOF at the moiré pore region, regardless of tip-sample distance, (ii) a Mott insulating phase for the MOF at the moiré wire region for large tip-sample distances (i.e., where the DBTJ effect is negligible), and (iii) a metallic phase at the moiré wire region for a specific reduced tip-sample distance range (i.e., where the DBTJ effect leads to a reduction in the population of MOF electronic states).This is the main message of our manuscript.Our study is not trying to say anything further on the nature of the quantum ground state other than classifying it as metallic or insulating.A quantitative reproduction based on DMFT of our experimental dI/dV spectra for all experimental variables (e.g., wide energy range including energies far away from the Fermi level; all locations with respect to hBN/Cu(111) moire pattern; wide range of tip-sample distances) is beyond the scope of our work.
We have now updated our manuscript to clarify these points (lines 222-225 on p. 9, and lines 307-317 on p. 12-13 in the main text) According to the authors "the DMFT calculations assume a uniform chemical potential for an infinite system, omitting effects of locality; this assumption is reasonable for the Mott insulating phase (i.e.localized states)".I think this assumption is wrong, the Mott insulator occurs because itinerant electrons are located by electronic correlations, so the calculation cannot be local, although the result is that the conduction electrons end up localized and prevented from moving.
We acknowledge that this statement could be clearer.Dynamical mean-field theory (DMFT) is a well-established -widely regarded as the goldstandard -method for understanding Mott metal-insulator transitions.It is not a local method.It fully describes both the Mott insulating and metallic phases, and is responsible for the fundamental understanding of strongly correlated metals 1-3

Let us give a little more technical detail of how DMFT works. Effects of electronic correlations can be accounted for via the self-energy, which in general is nonlocal (i.e., depends on wavevector k), but also intractable to calculate in almost all cases. DMFT calculations assume a self-energy which is local (i.e., independent of k): this makes the calculation of the self-energy feasible. The resulting interacting Green's function is still nonlocal, with local (on-site) correlation effects being fully accounted for (and nonlocal correlation effects being ignored). DMFT calculations do not omit the itinerant nature of electrons; DMFT calculations can still result in metallic phases with itinerant electrons. It is well established that DMFT with such a local approximation of the self-energy captures electronic correlations explicitly, and describes the Mott metal-insulator transition faithfully (see Refs. 38-41 in main text).
Our DMFT calculations assume an infinite, perfectly crystalline, defect-free 2D DCA3Cu2 MOF with a uniform chemical potential EF.Indeed, as stated above, DMFT calculations on systems with large unit cells -such as the long-range moiré unit cell of DCA3Cu2 on hBN/Cu(111) -are computationally challenging, if not intractable.Approximating the potential at each point in space as being uniform is similar in spirit to (but much more accurate than) the local density approximation (LDA) in DFT, where the charge density is locally assumed to be homogeneous.Nevertheless, the LDA can still describe inhomogeneous systems.Now, for EF = 0.25 to 0.5 eV in Supplementary Fig. S2b (corresponding to half-filling of the 2D kagome system), our DMFT calculations of the MOF spectral function indicate a Mott insulating phase, with a Mott gap Eg = ~200 meV (for an on-site Coulomb repulsion energy U = 0.65 eV; see also k-resolved spectral function for EF = 0.4 eV in Supplementary Fig. S5).Because this Mott phase is stable over this range of chemical potentials, it is robust to significant variations of the chemical potential, up to 0.25 eV.Furthermore, in this Mott insulating phase, electronic states are localised at the kagome sites, confined within areas that are small in length compared to the distance between nearestneighbour kagome sites. 4  In our experiments, the periodicity of the hBN/Cu(111) moiré domains considered (λ > 5 nm) is significantly larger than the distance between nearest-neighbour kagome sites (~1 nm).This moiré pattern imposes to the MOF a periodic modulation of the local work function, with a peak-to-peak modulation amplitude of ~0.2 eV for a modulation periodicity λ ≈ 12.5 nm (see Fig. 3 in main text).The amplitude of this local work function modulation becomes smaller with decreasing λ (Supplementary Fig. S22).That is, the MOF is exposed to a periodic modulation of the local electrostatic potential, which varies 'slowly' across the molecular kagome lattice.So, if the MOF is in the Mott insulating phase, the effect of such long-range electrostatic modulation on the localised electronic states is to shift the energy of these localised states accordingly: as long as the electrostatic modulation amplitude does not reach a critical value for the transition to the metallic phase, there is no other dramatic qualitative effect on such localised electronic states.This is consistent with the DMFT-calculated spectral functions in Supplementary Fig. S2b, where the LHB and UHB shift in energy when EF is varied between 0.25 and 0.5 eV, without other significant qualitative changes.This is also consistent with the experimental dI/dV spectra for the moiré pore regions in Fig. 3b of the main text, where the energy of the LHB and UHB is modulated following the moiré variation in local work function.
In other words, the Mott insulating phase is insensitive to the modulation of the local electrostatic potential, as long as the amplitude of this modulation remains below the threshold for the transition to the metal phase, and as long as the periodicity of this modulation is larger than the distance between nearest-neighbour kagome sites.Importantly, this means that the DMFT calculations for an infinite system in the Mott insulating phase capture the experimental phenomena observed locally at the moiré pore (regardless of tip-sample distance) and wire (for large tip-sample distances) regions.
We have now clarified this by updating lines 639-671 (p. 26, 27) in the Methods section of the main text.
Finally, I don't understand why the authors use the existence of DBTJ in some cases and not in others.The MOF is deposited in an insulator on Cu(111), and the MOF presents a gap at the Fermi level, according to the authors a Mott gap, therefore I do not understand why in some cases it is considered that a DBJT exists and in other cases This is completely ignored without explanation.
We have revised our manuscript to more clearly explain the effect of the DBTJ on all our experimental measurements (lines 290-295 on p. 12, and lines 697-703 on p. 29 in main text).
Briefly, the DBTJ effect is intrinsic to and manifests itself in all STM measurements of the DCA3Cu2 MOF on hBN/Cu(111) system, with energy level shifts due to tip-sample distance variations regardless of the location on the sample (i.e., both at moiré wire and pore regions).
We argue that the DBTJ affects the MOF dI/dV spectra more strongly at the moiré wire regions than at the pore regions due to the larger local work function (Fig. 3c), which leads to a MOF LHBM which is closer to the Fermi level, with the MOF electronic states prone to depopulating and the LHBM energy level susceptible of charging as the tip-sample-distance is reduced.This depopulation of the MOF electronic states results in the transition from Mott insulating (with an energy gap at the Fermi level) to metal phase (with no gap at the Fermi level and an increase in Fermi-level dI/dV signal).This is stated explicitly on lines 274-297 (p. 11-12) of the main text.
As shown in Supplementary Sections S20 and S21, the DBTJ effect also manifests itself at the moiré pore regions, with energy level shifts of the LHBM and UHBM as a function of tipsample distance, similar to the moiré wire regions, and consistent with the DBTJ model.Due to the smaller local work function at these moiré pore regions (Fig. 3c), the Fermi level lies close to the centre of the MOF energy gap, further from the LHBM in comparison to the moiré wire regions (Fig. 3b, d).That is, the LHBM and UHBM at the moiré pore regions shift in energy as the tip-sample distance is reduced, yet these energy shifts do not lead to a depopulation of MOF electronic states or to a Mott insulator-to-metal transition (for the range of tip-sample distances considered).This is fully consistent with the DMFT calculations of MOF spectral functions in Supplementary Figs.S2b and S4, which show a Mott insulating phase for chemical potentials EF between ~0.25 to ~0.5 eV.This means that the Mott insulating phase can be robust to energy level shifts significantly larger than the energy level shifts due to the DBTJ effect (for the range of tip-sample distances considered; see Supplementary Section S4).
In other words, the DBTJ effect manifests itself at both moiré wire and pore regions, but given the local work function difference between these two types of regions, only at the wire regions the electronic properties of the MOF are dramatically altered (i.e., transition from Mott insulator to metallic phase) as the result of such an effect (within the range of tip-sample distances considered in our study).
vi) page 4 (lines 102-105): The authors should be transparent and mention that DCA3Cu2 2D-MOF (the very same systems as the one shown here) has already been grown (as a full monolayer) on top of a rather good decoupling layer of graphene on Ir(111) (ref.31).

- 6 DFT
band structures of MOF over wide energy range.a, Free-standing DCA3Cu2 MOF.b, DCA3Cu2 MOF on hBN/Cu(111).Blue circles: projections onto MOF states.k-resolved spectral function for free-standing DCA3Cu2 MOF, calculated by DMFT (U = 0.65 eV, t = 0.05 eV, EF = 0.4 eV, corresponding to half-filling).viii) The authors should provide STS performed on a larger voltage range (for instance from -2V to +2V) to see what happens to the additional kagome bands away from the Fermi level.Is there any strong molecular HOMO/LUMO or 2D-MOF valence/conduction band feature at lower/higher voltages, as already observed in ref. 33 and in A. Kumar et al.Nano Letters 18, 5596 (2018).The latter reference should be added since DCA3Co2 2D-MOF was grown on the rather good decoupling graphene layer on Ir(111), whereby a 2D-MOF band structure signature was already observed.
STS measurements over a broader energy window.Orange curve: DCA lobe site of MOF within a pore region of the hBN/Cu(111) moiré pattern.Grey curve: bare hBN/Cu(111) reference spectrum.Spectra normalised and offset for clarity.Orange curve acquired in two parts: setpoint of Vb = −1 V, It = 100 pA for data between -1 V and -500 mV; setpoint of Vb = −500 mV, It = 100 pA for the remaining bias range.Grey curve setpoint: Vb = −2 V, It = 100 pA.
shows dI/dV STS measurements at the edge of a 2D MOF domain, where DCA molecules are coordinated to only one Cu atom (and not two as within the MOF bulk).At these MOF edge sites, the dI/dV spectra show remnants of the Hubbard bands, with a weaker upper Hubbard band, and an additional peak at ~0.6 V, resembling the (uncoordinated) DCA LUMO on hBN [see D. Kumar et al. "Mesoscopic 2D molecular selfassembly on an insulator", Nanotechnology 34, 205601 (2023); updated Ref. 47].
a pore region of the hBN/Cu(111) moirée pattern.a, STM image of DCA3Cu2 MOF on hBN/Cu(111) (Vb = −1 V, It = 10 pA).b, STS measurements performed at positions corresponding to coloured markers in (a).Grey curve: reference spectrum acquired upon bare hBN/Cu(111).Curves offset for clarity.Dashed lines indicate position of dI/dV = 0. Tip height stabilised 150 pm further away from the surface with respect to a setpoint of Vb = 10 mV, It = 10 pA.dI/dV spectra at different moiré pore regions within hBN/Cu(111) domain with period λ ≈ 12.5 nm.a, Cu sites.b, DCA lobe sites.All acquisition sites close to centre of moiré pore regions.Spectra normalised and offset for clarity.Pore 1 setpoint: Vb = −500 mV, It = 500 pA.Pores 2,3 setpoints: 190 pm further from the surface with respect to setpoint of Vb = 10 mV, It = 10 pA.Pores 4,5 setpoint: 225 pm further from the surface with respect to setpoint of Vb = 10 mV, It = 10 pA.Pore 6 setpoint: 150 pm further from the surface with respect to setpoint of Vb = 10 mV, It = 10 pA.STS measurements at the edge of a DCA3Cu2 MOF domain.a, STM image of the edge of a MOF domain (Vb = −1 V, It = 10 pA).b, STS measurements at Cu sites (circle markers) and DCA lobe sites (triangle markers) both at the edge of the MOF domain (black) and within the MOF domain (red).Curves offset for clarity.Setpoints: Vb = −500 mV, It = 100 pA.STS measurements at a DCA3Cu2 MOF domain boundary.a, STM image showing a MOF domain boundary (Vb = −1 V, It = 10 pA).b, STS measurements at DCA lobe sites both at the MOF domain boundary (black) and within the MOF domain (red).Curves offset for clarity.Setpoints: Vb = −500 mV, It = 100 pA.STS measurements at Cu vacancy defect within a DCA3Cu2 MOF domain.a, STM image showing a Cu vacancy defect (Vb = −1 V, It = 10 pA).b, STS measurements at Cu sites in proximity of Cu vacancy (green and orange), and at Cu vacancy (blue).Curves offset for clarity.Setpoints: 135 pm further away from the surface with respect to a setpoint of Vb = 10 mV, It = 10 pA.Tip-induced gating at a Cu site of the MOF within a wire region of the hBN/Cu(111) moiré pattern.a, dI/dV spectra at MOF Cu site, for different ∆z + z0 (z0 given by STM setpoint Vb = 10 mV, It = 10 pA).Purple circles (red squares): MOF charging peak (intrinsic electronic state at MOF band edge, respectively).Spectra normalised and offset for clarity.b, Vcharge [purple circles in (a)] and Vstate [red squares in (a)] as a function of ∆z.Black solid lines: global fits to Eqs. (1) and (2) in main text.c, dI/dV signal at Fermi level (Vb = 0) as a function of ∆z, from (a).Increased dI/dV (Vb = 0) indicates metallic phase.Inset: STM image with position where dI/dV (∆z) were performed indicated by blue circle (Vb = −1 V, It = 10 pA).dI/dV spectroscopy for Cu site of MOF within a pore region of hBN/Cu(111) moiré pattern.a, dI/dV spectra for different tip-sample distances ∆z+z0 (z0 represents tip-sample distance for STM setpoint of Vb = 10 mV, It = 10 pA) at a Cu site [location indicated by red circle in (c)].Red squares (circles) indicate LHBM (UHBM, respectively).b, LHBM and UHBM as a function of ∆z, from (a).Black dashed curves: fits based on Eqs.(S7) and (S8).c, STM image of DCA3Cu2 on hBN/Cu(111).Red circle indicates position where spectra shown in (a) were acquired (Vb = −1 V, It = 10 pA).xv) Figure S10.It is not clear at all that the charging rings are increasing their perimeter around the DCA molecule (see ref. 31).It looks just the same intensity at the Cu positions.
Fig. S23.dI/dV maps of DCA3Cu2/hBN/Cu(111): charging ring.a, STM image of DCA3Cu2 at a wire region of hBN/Cu(111) moiré pattern (Vb = −1 V, It = 10 pA).b-m, dI/dV maps of region in (a), at indicated bias voltages Vb, obtained via numerical derivative of pixel-by-pixel I(V) curves.At each pixel, the tip-sample distance was stabilised 300 pm further away from the surface relative to a setpoint of Vb = 10 mV, It = 10 pA, before I(V) acquisition.Scale bars: 1 nm.
Charging features at a pore-wire boundary of the moiré pattern.a, STM image of MOF/hBN/Cu(111) showing two pore regions and one wire region of the hBN/Cu(111) moiré pattern (Vb = −1 V, It = 10 pA).b, dI/dV spectra for different tip-sample changes (∆z), acquired at MOF Cu site, as indicated in (a).Spectra normalised and offset for clarity.Setpoints range between 250 pm further from surface (bottom curve) to 105 pm further from surface (top curve) with respect to a setpoint of Vb = 10 mV, It = 10 pA.
STS measurements at the edge of aDCA3Cu2 MOF domain.a, STM image of the edge of a MOF domain (Vb = −1 V, It = 10 pA).b, STS measurements at Cu sites (circle markers) and DCA lobe sites (triangle markers) both at the edge of the MOF domain (black) and within the MOF domain (red).Curves offset for clarity.Setpoints: Vb = −500 mV, It = 100 pA.STS measurements at a DCA3Cu2 MOF domain boundary.a, STM image showing a MOF domain boundary (Vb = −1 V, It = 10 pA).b, STS measurements at DCA lobe sites both at the MOF domain boundary (black) and within the MOF domain (red).Curves offset for clarity.Setpoints: Vb = −500 mV, It = 100 pA.STS measurements at Cu vacancy defect a DCA3Cu2 MOF domain.a, STM image showing a Cu vacancy defect (Vb = −1 V, It = 10 pA).b, STS measurements at Cu sites in proximity of Cu vacancy (green and orange), and at Cu vacancy (blue).Curves offset for clarity.Setpoints: 135 pm further away from the surface with respect to a setpoint of Vb = 10 mV, It = 10 pA.The authors have convincingly answered all my questions.The work is more clearly presented and well supported with new additional experimental results and theoretical simulations.I therefore recommend it for publication in Nature Communications.Minor typos: Line 175: Fig. S14 Fig. S19 or Section S14 Line 201: Fig. 3c, 3b Reviewer #2 (Remarks to the Author): by Yan et al.).The size of this image is ~four times the size of any image in previous Ref.31, with similar MOF quality despite the insulating substrate (compared to a conductive substrate in previous Ref.31).The bright islands are indeed excess Cu clusters forming after the final annealing step in our sample preparation; similar bright clusters are also present in previous Ref.31.We have added a comment to the main text explicitly identifying these as Cu.
of previous Ref.31).That is, graphene is not a perfectly decoupling layer.In contrast, it is well established that electronic states of molecular and metal-organic systems on wide bandgap, single-layer hBN retain their intrinsic properties and remain unhybridized with substrate states, within a relatively large energy range (~5 eV) around the Fermi level (see previous Ref.30 by Auwarter et al., updated Ref. 33, and Fig.